Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant linear correlation between advertising cost and profit . Use a significance level of 0.01 and round all values to 4 decimal places. Advertising Cost Profit 3 19 4 24 5 21 6 24 7 28 8 28 Ho: ρ = 0 Ha: ρ ≠ 0 Find the Linear Correlation Coefficient r = Find the p-value p-value =
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant
| Advertising Cost | Profit |
|---|---|
| 3 | 19 |
| 4 | 24 |
| 5 | 21 |
| 6 | 24 |
| 7 | 28 |
| 8 | 28 |
Ho: ρ = 0
Ha: ρ ≠ 0
Find the Linear
r =
Find the p-value
p-value =
State the hypotheses.
That is, there is no significant linear correlation between advertising cost and profit.
That is, there is significant linear correlation between advertising cost and profit.
Use EXCEL to obtain the value correlation coefficient r:
EXCEL procedure:
- Go to EXCEL
- Go to Data>Data Analysis.
- Choose Correlation.
- Enter the range as $A$1:$B$7.
- Check the option Labels in First row.
- Click OK.
EXCEL output:
From the EXCEL output, the value of the correlation coefficient is 0.8827.
Thus, the value of correlation coefficient is 0.8827.
Obtain the value of the test statistic.
The formula of the test statistic is,
Thus, the value of the test statistic is 3.7567.
Step by step
Solved in 3 steps with 6 images
